This paper is concerned with a special class of unit memory convolutional codes (UMCCs), called block oriented UMCCs (BOUMCCs). Distinguished from conventional UMCCs, which usually have small constraint lengths, the BOUMCCs have relatively large constraint lengths. We conduct the performance analysis by assuming a first-order Markov model, which indicates that the performance of the BOUMCCs depends critically on both the error propagation and the sub-frame error rate of the first layer. The error propagation can be alleviated by the use of partial superposition, which is specified by a superposition matrix with a fraction of columns being nulled. Given a superposition fraction, we propose a tree growing and pruning algorithm (TGPA) with a tunable sliding window, which provides a convenient way to trade off the decoding delay and the performance. We also present a structured construction and show by simulation that there is no performance degradation compared with random construction. Numerical results also show that, by taking the TBCCs as basic codes, the performance of BOUMCCs with TGPA is comparable to that of other short codes but with a more flexible construction or a lower complexity.

In this paper, we propose a systematic low density generator matrix (LDGM) code ensemble, which is defined by the Bernoulli process. We prove that, under maximum likelihood (ML) decoding, the proposed ensemble can achieve the capacity of binary-input output symmetric (BIOS) memoryless channels in terms of bit error rate (BER). The proof technique reveals a new mechanism, different from lowering down frame error rate (FER), that the BER can be lowered down by assigning light codeword vectors to light information vectors. The finite length performance is analyzed by deriving an upper bound and a lower bound, both of which are shown to be tight in the high signal-to-noise ratio (SNR) region. To improve the waterfall performance, we construct the systematic convolutional LDGM (SysConv-LDGM) codes by a random splitting process. The SysConv-LDGM codes are easily configurable in the sense that any rational code rate can be realized without complex optimization. As a universal construction, the main advantage of the SysConv-LDGM codes is their near-capacity performance in the waterfall region and predictable performance in the error-floor region that can be lowered down to any target as required by increasing the density of the uncoupled LDGM codes. Numerical results are also provided to verify our analysis.

This paper is concerned with block Markov superposition transmission (BMST) of tail-biting convolutional code (TBCC). We propose a new decoding algorithm for BMST-TBCC, which integrates a serial list Viterbi algorithm (SLVA) with a soft check instead of conventional cyclic redundancy check (CRC). The basic idea is that, compared with an erroneous candidate codeword, the correct candidate codeword for the first sub-frame has less influence on the output of Viterbi algorithm for the second sub-frame. The threshold is then determined by statistical learning based on the introduced empirical divergence function. The numerical results illustrate that, under the constraint of equivalent decoding delay, the BMST-TBCC has comparable performance with the polar codes. As a result, BMST-TBCCs may find applications in the scenarios of the streaming ultra-reliable and low latency communication (URLLC) data services.

In this paper, we present a new class of spatially coupled low-density parity-check (SC-LDPC) codes, which are constructed by sending codewords of LDPC block code (LDPCBC) in a block Markov superposition transmission (BMST) manner. Different from the conventional SC-LDPC codes, the proposed SC-LDPC codes can have encoder/decoder implemented with the basis of the hardware components of the corresponding LDPC-BCs. The proposed SC-LDPC codes are also a special class of BMST-LDPC codes. Distinguished from other types of BMST codes, BMST-LDPC codes have lower error floors even with an encoding memory of one and hence have lower decoding latency. Also different from the original BMST codes, partial superposition is implemented to alleviate error propagation. To analyze the bit error rate (BER) performance, we present the genie-aided (GA) bounds, which can be obtained by simulation or estimated from the performance of the basic code. Numerical results are presented to validate our analysis and demonstrate the performance advantage of the BMST-LDPC codes over the LDPC-BCs.

This paper is concerned with three ensembles of systematic low density generator matrix (LDGM) codes, all of which were provably capacity-achieving in terms of bit error rate (BER). This, however, does not necessarily imply that they achieve the capacity in terms of frame error rate (FER), as seen from a counterexample constructed in this paper. We then show that the first and second ensembles are capacity-achieving under list decoding over binary-input output symmetric (BIOS) memoryless channels. We point out that, in principle, the equivocation due to list decoding can be removed with negligible rate loss by the use of the concatenated codes. Simulation results show that the considered convolutional (spatially-coupled) LDGM code is capacity-approaching with an iterative belief propagation decoding algorithm.